qu.env.lastSaved= Aug 2, 2005 12:04:12 AM @ qu.env.validTest= false @ qu.1.topic=5_1 Add Fractions with C.D.@ qu.1.1.mode=Blanks@ qu.1.1.name=+ +@ qu.1.1.comment=Evaluate:
$n1
  + 
$n2
  = 
$d1
$d2

Write the answer as an integer or fraction in lowest terms similar to 9/5.

The fraction has a common denominator. Add the numerators.

$n1 + $n2
 = 
$d1

${$n1 + $n2}
 = 
$d1

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}

$n
  
$d

or ${$frac($n,$d)}@ qu.1.1.editing=useHTML@ qu.1.1.algorithm=$d1=range(2,15,1); $d2=$d1; $n1=range(1,15,1); $n2=range(1,15,1); condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); condition:ne($n1+$n2,0);$cf=$gcd(abs($n1+$n2),$d1); $n=($n1+$n2)/$cf; $d=$d1/$cf;@ qu.1.1.question= Evaluate :
$n1
+
$n2
= <1>
$d1
$d2

Write the answer as an integer or fraction in lowest terms similar to 9/5.

@ qu.1.1.blank.1=%24%7bfrac%28%24n%2c%24d%29%7d@ qu.1.1.extra=@ qu.1.1.format.input=text@ qu.1.2.mode=Blanks@ qu.1.2.name=+ -@ qu.1.2.comment=Evaluate:
$n1
  + 
$n2
  = 
$d1
$d2

Write the answer as an integer or fraction in lowest terms similar to 9/5.

The fraction has a common denominator. Add the numerators.

$n1 + ($n2)
 = 
$d1

${$n1 + $n2}
 = 
$d1

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}

$n
  
$d

or ${$frac($n,$d)} @ qu.1.2.editing=useHTML@ qu.1.2.algorithm=$d1=range(2,15,1); $d2=$d1; $n1=range(1,15,1); $n2=range(-15,-1,1); condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); condition:ne($n1+$n2,0);$cf=$gcd(abs($n1+$n2),$d1); $n=($n1+$n2)/$cf; $d=$d1/$cf;@ qu.1.2.question= Evaluate :
$n1
+
$n2
= <1>
$d1
$d2

Write the answer as an integer or fraction in lowest terms similar to 9/5.

@ qu.1.2.blank.1=%24%7bfrac%28%24n%2c%24d%29%7d@ qu.1.2.extra=@ qu.1.2.format.input=text@ qu.1.3.mode=Blanks@ qu.1.3.name=- -@ qu.1.3.comment=Evaluate:
$n1
  + 
$n2
  = 
$d1
$d2

Write the answer as an integer or fraction in lowest terms similar to 9/5.

The fraction has a common denominator. Add the numerators.

$n1 + ($n2)
 = 
$d1

${$n1 + $n2}
 = 
$d1

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}

$n
  
$d

or ${$frac($n,$d)} @ qu.1.3.editing=useHTML@ qu.1.3.algorithm=$d1=range(2,15,1); $d2=$d1; $n1=range(-15,-1,1); $n2=range(-15,-1,1); condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); condition:ne($n1+$n2,0); $cf=$gcd(abs($n1+$n2),$d1); $n=($n1+$n2)/$cf; $d=$d1/$cf;@ qu.1.3.question= Evaluate :
$n1
+
$n2
= <1>
$d1
$d2

Write the answer as an integer or fraction in lowest terms similar to 9/5.

@ qu.1.3.blank.1=%24%7bfrac%28%24n%2c%24d%29%7d@ qu.1.3.extra=@ qu.1.3.format.input=text@ qu.1.4.mode=Blanks@ qu.1.4.name=- +@ qu.1.4.comment=Evaluate:
$n1
  + 
$n2
  = 
$d1
$d2

Write the answer as an integer or fraction in lowest terms similar to 9/5.

The fraction has a common denominator. Add the numerators.

$n1 + $n2
 = 
$d1

${$n1 + $n2}
 = 
$d1

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}

$n
  
$d

or ${$frac($n,$d)}@ qu.1.4.editing=useHTML@ qu.1.4.algorithm=$d1=range(2,15,1); $d2=$d1; $n1=-1*range(1,15,1); $n2=range(1,15,1); condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); condition:ne($n1+$n2,0); $cf=$gcd(abs($n1+$n2),$d1); $n=($n1+$n2)/$cf; $d=$d1/$cf;@ qu.1.4.question= Evaluate :
$n1
+
$n2
= <1>
$d1
$d2

Write the answer as an integer or fraction in lowest terms similar to 9/5.

@ qu.1.4.blank.1=%24%7bfrac%28%24n%2c%24d%29%7d@ qu.1.4.extra=@ qu.1.4.format.input=text@ qu.2.topic=5_1 Subtract Fractions with C.D.@ qu.2.1.mode=Blanks@ qu.2.1.name=+ +@ qu.2.1.comment=

Evaluate:
$n1
  − 
$n2
 =
$d1
$d2

Write the answer as an integer or fraction in lowest terms similar to 9/5.

The fraction has a common denominator. Add the numerators.

$n1 − $n2
=
$d1

${$n1-$n2}
=
$d1

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}

$n
$d

or ${$frac($n,$d)}@ qu.2.1.editing=useHTML@ qu.2.1.algorithm=$d1=range(2,15,1); $d2=$d1; $n1=range(1,15,1); $n2=range(1,15,1); condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); condition:ne($n1-$n2,0); $cf=$gcd(abs($n1-$n2),$d1); $n=($n1-$n2)/$cf; $d=$d1/$cf;@ qu.2.1.question= Evaluate :
$n1
−
$n2
= <1>
$d1
$d2

Write the answer as an integer or fraction in lowest terms similar to 9/5.

@ qu.2.1.blank.1=%24%7bfrac%28%24n%2c%24d%29%7d@ qu.2.1.extra=@ qu.2.1.format.input=text@ qu.2.2.mode=Blanks@ qu.2.2.name=+ -@ qu.2.2.comment=

Evaluate:

$n1
  − 
$n2
 =
$d1
$d2

Write the answer as an integer or fraction in lowest terms similar to 9/5.

The fraction has a common denominator. Add the numerators.

$n1 − ($n2)
=
$d1

${$n1-$n2}
=
$d1

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}

$n
$d

or ${$frac($n,$d)}@ qu.2.2.editing=useHTML@ qu.2.2.algorithm=$d1=range(2,15,1); $d2=$d1; $n1=range(1,15,1); $n2=range(-15,-1,1); condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); condition:ne($n1-$n2,0); $cf=$gcd(abs($n1-$n2),$d1); $n=($n1-$n2)/$cf; $d=$d1/$cf;@ qu.2.2.question= Evaluate :
$n1
−
$n2
= <1>
$d1
$d2

Write the answer as an integer or fraction in lowest terms similar to 9/5.

@ qu.2.2.blank.1=%24%7bfrac%28%24n%2c%24d%29%7d@ qu.2.2.extra=@ qu.2.2.format.input=text@ qu.2.3.mode=Blanks@ qu.2.3.name=- -@ qu.2.3.comment=

Evaluate:

$n1
  − 
$n2
 =
$d1
$d2

Write the answer as an integer or fraction in lowest terms similar to 9/5.

The fraction has a common denominator. Add the numerators.

$n1 − ($n2)
=
$d1

${$n1 - $n2}
=
$d1

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}

$n
$d

or ${$frac($n,$d)}@ qu.2.3.editing=useHTML@ qu.2.3.algorithm=$d1=range(2,15,1); $d2=$d1; $n1=range(-15,-1,1); $n2=range(-15,-1,1); condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); condition:ne($n1-$n2,0); $cf=$gcd(abs($n1-$n2),$d1); $n=($n1-$n2)/$cf; $d=$d1/$cf;@ qu.2.3.question= Evaluate :
$n1
−
$n2
= <1>
$d1
$d2

Write the answer as an integer or fraction in lowest terms similar to 9/5.

@ qu.2.3.blank.1=%24%7bfrac%28%24n%2c%24d%29%7d@ qu.2.3.extra=@ qu.2.3.format.input=text@ qu.2.4.mode=Blanks@ qu.2.4.name=- +@ qu.2.4.comment=

Evaluate:

$n1
  − 
$n2
 =
$d1
$d2

Write the answer as an integer or fraction in lowest terms similar to 9/5.

The fraction has a common denominator. Add the numerators.

$n1 − $n2
=
$d1

${$n1 - $n2}
=
$d1

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}

$n
$d

or ${$frac($n,$d)}@ qu.2.4.editing=useHTML@ qu.2.4.algorithm=$d1=range(2,15,1); $d2=$d1; $n1=-1*range(1,15,1); $n2=range(1,15,1); condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); condition:ne($n1-$n2,0); $cf=$gcd(abs($n1-$n2),$d1); $n=($n1-$n2)/$cf; $d=$d1/$cf;@ qu.2.4.question= Evaluate :
$n1
−
$n2
= <1>
$d1
$d2

Write the answer as an integer or fraction in lowest terms similar to 9/5.

@ qu.2.4.blank.1=%24%7bfrac%28%24n%2c%24d%29%7d@ qu.2.4.extra=@ qu.2.4.format.input=text@ qu.3.topic=5_1 Review - Improper to Mixed@ qu.3.1.mode=Blanks@ qu.3.1.name=+@ qu.3.1.comment=

Write the improper fraction as a mixed fraction by filling in the boxes.

$n1
$d
= $w
$n
$d

Divide $n1 by $d. Find the quotient and remainder.
$n1 ÷ $d = $w with a remainder of $n.
The mixed fraction is:
$w
$n
$d
@ qu.3.1.editing=useHTML@ qu.3.1.algorithm=$d=range(2,11,1); $w=range(2,5,1); $n=range(1,$d-1,1); condition:eq(gcd($d,$n),1); $n1=$w*$d+$n@ qu.3.1.question=

Write the improper fraction as a mixed fraction by filling in the boxes.

$n1
$d
= <1>
<2>
<3>
@ qu.3.1.blank.1=%24w@ qu.3.1.blank.2=%24n@ qu.3.1.blank.3=%24d@ qu.3.1.extra=@ qu.3.1.format.input=text@ qu.3.2.mode=Blanks@ qu.3.2.name=-@ qu.3.2.comment=

Write the improper fraction as a mixed fraction by filling in the boxes.

$n1
$d
= $w
$n
$d

Divide $n1 by $d. Find the quotient and remainder.
$n1 ÷ $d = $w with a remainder of -$n.
The mixed fraction is:
$w
$n
$d
@ qu.3.2.editing=useHTML@ qu.3.2.algorithm=$d=range(2,11,1); $w=-1*range(2,5,1); $n=range(1,$d-1,1); condition:eq(gcd($d,$n),1); $n1=$w*$d-$n;@ qu.3.2.question=

Write the improper fraction as a mixed fraction by filling in the boxes.

$n1
$d
= <1>
<2>
<3>
@ qu.3.2.blank.1=%24w@ qu.3.2.blank.2=%24n@ qu.3.2.blank.3=%24d@ qu.3.2.extra=@ qu.3.2.format.input=text@ qu.4.topic=5_1 Add/Subtract Mixed Frac w C.D.@ qu.4.1.mode=Blanks@ qu.4.1.name=+ +@ qu.4.1.comment=Evaluate:
$w1
$n1
  + $w2
$n2
  =
$d1
$d2

Write your answer as a mixed fraction filling in the boxes.

Write the mixed fractions as improper fractions.

${$w1*$d1+$n1}
  + 
${$w2*$d2+$n2}
  =
$d1
$d2

The fractions have a common denominator. Add the fractions.
${$w1*$d1+$n1+$w2*$d2+$n2}
 = 
$d1

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}
${($w1*$d1+$n1+$w2*$d2+$n2)/$cf}
 = 
${$d1/$cf}

Write the fraction in mixed form.

$w
$n
  
$d
@ qu.4.1.editing=useHTML@ qu.4.1.algorithm=$w1=range(2,5,1); $w2=range(2,5,1); $d1=range(2,15,1); $d2=$d1; $n1=range(1,$d1-1,1); $n2=range(1,$d2-1,1); condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); $cf=$gcd(abs(($w1*$d1+$n1)+($w2*$d2+$n2)),$d1); $na=(($w1*$d1+$n1)+($w2*$d2+$n2))/$cf; $d=$d1/$cf; $w=int($na/$d); $n=$na-$w*$d; condition:ne($n,0);@ qu.4.1.question=

Evaluate :

$w1
$n1
+ $w2
$n2
= <1> <2>
$d1
$d2
<3>

Write your answer as a mixed fraction filling in the boxes.

@ qu.4.1.blank.1=%24w@ qu.4.1.blank.2=%24n@ qu.4.1.blank.3=%24d@ qu.4.1.extra=@ qu.4.1.format.input=text@ qu.4.2.mode=Blanks@ qu.4.2.name=- +@ qu.4.2.comment=

Evaluate:

$w1
$n1
 + $w2
$n2
 =
$d1
$d2

Write your answer as a mixed fraction filling in the boxes.

Write the mixed fractions as improper fractions.

${$w1*$d1-$n1}
 +
${$w2*$d2+$n2}
 =
$d1
$d2

The fractions have a common denominator. Add the fractions.
${$w1*$d1-$n1+$w2*$d2+$n2}
=
$d1

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}
${($w1*$d1-$n1+$w2*$d2+$n2)/$cf}
=
${$d1/$cf}

Write the fraction in mixed form.

$w
$n
$d
@ qu.4.2.editing=useHTML@ qu.4.2.algorithm=$w1=-1*range(2,5,1); $w2=range(2,5,1); $d1=range(2,15,1); $d2=$d1; $n1=range(1,$d1-1,1); $n2=range(1,$d2-1,1); condition:ne($n1,$n2); condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); $num=($w1*$d1-$n1)+($w2*$d2+$n2); condition:ne($num,0); $cf=$gcd(abs($num),$d1); $d=$d1/$cf; $pna=abs($num)/$cf; $wt=int($pna/$d); $n=$pna-$wt*$d; condition:ne($n,0); $w=if(lt($num,0),-1*$wt,$wt); condition:ne($w,0);@ qu.4.2.question= Evaluate :
$w1
$n1
$d1
+ $w2
$n2
$d2
= <1>
<2>
<3>

Write your answer as a mixed fraction filling in the boxes.

@ qu.4.2.blank.1=%24w@ qu.4.2.blank.2=%24n@ qu.4.2.blank.3=%24d@ qu.4.2.extra=@ qu.4.2.format.input=text@ qu.4.3.mode=Blanks@ qu.4.3.name=+ -@ qu.4.3.comment=

Evaluate:

$w1
$n1
 - $w2
$n2
 =
$d1
$d2

Write your answer as a mixed fraction filling in the boxes.

Write the mixed fractions as improper fractions.

${$w1*$d1+$n1}
 - 
${$w2*$d2+$n2}
 =
$d1
$d2

The fractions have a common denominator. Add the fractions.
${$w1*$d1+$n1-($w2*$d2+$n2)}
=
$d1

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}
${($w1*$d1+$n1-($w2*$d2+$n2))/$cf}
=
${$d1/$cf}

Write the fraction in mixed form.

$w
$n
$d
@ qu.4.3.editing=useHTML@ qu.4.3.algorithm=$w1=range(2,5,1); $w2=range(2,5,1); $d1=range(2,15,1); $d2=$d1; $n1=range(1,$d1-1,1); $n2=range(1,$d2-1,1); condition:ne($n1,$n2); condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); $num=($w1*$d1+$n1)-($w2*$d2+$n2); condition:ne($num,0); $cf=$gcd(abs($num),$d1); $d=$d1/$cf; $pna=abs($num)/$cf; $wt=int($pna/$d); $n=$pna-$wt*$d; condition:ne($n,0); $w=if(lt($num,0),-1*$wt,$wt); condition:ne($w,0);@ qu.4.3.question= Evaluate :
$w1
$n1
$d1
− $w2
$n2
$d2
= <1>
<2>
<3>

Write your answer as a mixed fraction filling in the boxes.

@ qu.4.3.blank.1=%24w@ qu.4.3.blank.2=%24n@ qu.4.3.blank.3=%24d@ qu.4.3.extra=@ qu.4.3.format.input=text@ qu.4.4.mode=Blanks@ qu.4.4.name=- -@ qu.4.4.comment=

Evaluate:

$w1
$n1
 - $w2
$n2
 =
$d1
$d2

Write your answer as a mixed fraction filling in the boxes.

Write the mixed fractions as improper fractions.

${$w1*$d1-$n1}
 -
${$w2*$d2+$n2}
 =
$d1
$d2

The fractions have a common denominator. Add the fractions.
${$w1*$d1-$n1-($w2*$d2+$n2)}
=
$d1

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}
${($w1*$d1-$n1-($w2*$d2+$n2))/$cf}
=
${$d1/$cf}

Write the fraction in mixed form.

$w
$n
$d
@ qu.4.4.editing=useHTML@ qu.4.4.algorithm=$w1=-1*range(2,5,1); $w2=range(2,5,1); $d1=range(2,15,1); $d2=$d1; $n1=range(1,$d1-1,1); $n2=range(1,$d2-1,1); condition:ne($n1,$n2); condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); $num=($w1*$d1-$n1)-($w2*$d2+$n2); condition:ne($num,0); $cf=$gcd(abs($num),$d1); $d=$d1/$cf; $pna=abs($num)/$cf; $wt=int($pna/$d); $n=$pna-$wt*$d; condition:ne($n,0); $w=if(lt($num,0),-1*$wt,$wt); condition:ne($w,0);@ qu.4.4.question= Evaluate :
$w1
$n1
$d1
− $w2
$n2
$d2
= <1>
<2>
<3>

Write your answer as a mixed fraction filling in the boxes.

@ qu.4.4.blank.1=%24w@ qu.4.4.blank.2=%24n@ qu.4.4.blank.3=%24d@ qu.4.4.extra=@ qu.4.4.format.input=text@ qu.5.topic=5_2 Add/Subtract Mixed Fractions@ qu.5.1.mode=Blanks@ qu.5.1.name=+ +@ qu.5.1.comment=

Evaluate:

$w1
$n1
 + $w2
$n2
 =
$d1
$d2

Write the mixed fractions as improper fractions.

${$w1*$d1+$n1}
 +
${$w2*$d2+$n2}
 =
$d1
$d2

Write with a common denominator.
${($w1*$d1+$n1)*$lcd/$d1}
 +
${($w2*$d2+$n2)*$lcd/$d2}
 =
$lcd
$lcd

Add the fractions.
${($w1*$d1+$n1)*$lcd/$d1+($w2*$d2+$n2)*$lcd/$d2}
=
$lcd

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}
${(($w1*$d1+$n1)*$lcd/$d1+($w2*$d2+$n2)*$lcd/$d2)/$cf}
=
${$lcd/$cf}

Write the fraction in mixed form.

$w
$n
$d
@ qu.5.1.editing=useHTML@ qu.5.1.algorithm=$w1=range(2,5,1); $w2=range(2,5,1); $d1=range(2,8,1); $d2=range(2,8,1); condition:ne($d1,$d2); $lcd=($d1*$d2)/gcd($d1,$d2); $n1=range(1,$d1-1,1); $n2=range(1,$d2-1,1); condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); $cf=$gcd(abs(($w1*$d1+$n1)*$lcd/$d1+($w2*$d2+$n2)*$lcd/$d2),$lcd); $na=(($w1*$d1+$n1)*$lcd/$d1+($w2*$d2+$n2)*$lcd/$d2)/$cf; $d=$lcd/$cf; $w=int($na/$d); $n=$na-$w*$d; condition:ne($n,0);@ qu.5.1.question= Evaluate :
$w1
$n1
+ $w2
$n2
= <1>
<2>
$d1
$d2
<3>

Write your answer as a mixed fraction filling in the boxes.

@ qu.5.1.blank.1=%24w@ qu.5.1.blank.2=%24n@ qu.5.1.blank.3=%24d@ qu.5.1.extra=@ qu.5.1.format.input=text@ qu.5.2.mode=Blanks@ qu.5.2.name=- +@ qu.5.2.comment=

Evaluate:

$w1
$n1
 + $w2
$n2
 =
$d1
$d2

Write the mixed fractions as improper fractions.

${$w1*$d1-$n1}
 +
${$w2*$d2+$n2}
 =
$d1
$d2

Write the fractions with a common denominator.
$num1
 +
$num2
 =
$lcd
$lcd

Add the fractions.
$num
 =
$lcd

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}
${$num/$cf}
=
${$lcd/$cf}

Write the fraction in mixed form.

$w
$n
$d
@ qu.5.2.editing=useHTML@ qu.5.2.algorithm=$w1=-1*range(2,5,1); $w2=range(2,5,1); $d1=range(2,8,1); $d2=range(2,8,1); condition:ne($d1,$d2); $lcd=($d1*$d2)/gcd($d1,$d2); $n1=range(1,$d1-1,1); $n2=range(1,$d2-1,1); condition:ne($n1,$n2); condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); $num1=($w1*$d1-$n1)*$lcd/$d1; $num2=($w2*$d2+$n2)*$lcd/$d2; $num=$num1+$num2; condition:ne($num,0); $cf=$gcd(abs($num),$lcd); $d=$lcd/$cf; $pna=abs($num)/$cf; $wt=int($pna/$d); $n=$pna-$wt*$d; condition:ne($n,0); $w=if(lt($num,0),-1*$wt,$wt); condition:ne($w,0);@ qu.5.2.question= Evaluate :
$w1
$n1
$d1
+ $w2
$n2
$d2
= <1>
<2>
<3>

Write your answer as a mixed fraction filling in the boxes.

@ qu.5.2.blank.1=%24w@ qu.5.2.blank.2=%24n@ qu.5.2.blank.3=%24d@ qu.5.2.extra=@ qu.5.2.format.input=text@ qu.5.3.mode=Blanks@ qu.5.3.name=+ -@ qu.5.3.comment=

Evaluate:

$w1
$n1
 - $w2
$n2
 =
$d1
$d2

Write the mixed fractions as improper fractions.

${$w1*$d1+$n1}
 - 
${$w2*$d2+$n2}
 =
$d1
$d2

Write the fractions with a common denominator.
$num1
 - 
$num2
 =
$lcd
$lcd

Add the fractions.
$num
 =
$lcd

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}
${$num/$cf}
=
${$lcd/$cf}

Write the fraction in mixed form.

$w
$n
$d
@ qu.5.3.editing=useHTML@ qu.5.3.algorithm=$w1=range(2,5,1); $w2=range(2,5,1); $d1=range(2,8,1); $d2=range(2,8,1); condition:ne($d1,$d2); $lcd=($d1*$d2)/gcd($d1,$d2); $n1=range(1,$d1-1,1); $n2=range(1,$d2-1,1); condition:ne($n1,$n2); condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); $num1=($w1*$d1+$n1)*$lcd/$d1; $num2=($w2*$d2+$n2)*$lcd/$d2; $num=$num1-$num2; condition:ne($num,0); $cf=$gcd(abs($num),$lcd); $d=$lcd/$cf; $pna=abs($num)/$cf; $wt=int($pna/$d); $n=$pna-$wt*$d; condition:ne($n,0); $w=if(lt($num,0),-1*$wt,$wt); condition:ne($w,0);@ qu.5.3.question= Evaluate :
$w1
$n1
$d1
− $w2
$n2
$d2
= <1>
<2>
<3>

Write your answer as a mixed fraction filling in the boxes.

@ qu.5.3.blank.1=%24w@ qu.5.3.blank.2=%24n@ qu.5.3.blank.3=%24d@ qu.5.3.extra=@ qu.5.3.format.input=text@ qu.5.4.mode=Blanks@ qu.5.4.name=- -@ qu.5.4.comment=

Evaluate:

$w1
$n1
 - $w2
$n2
 =
$d1
$d2

Write the mixed fractions as improper fractions.

${$w1*$d1-$n1}
 - 
${$w2*$d2+$n2}
 =
$d1
$d2

Write the fractions with a common denominator.
$num1
 - 
$num2
 =
$lcd
$lcd

Add the fractions.
$num
 =
$lcd

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}
${$num/$cf}
=
${$lcd/$cf}

Write the fraction in mixed form.

$w
$n
$d
@ qu.5.4.editing=useHTML@ qu.5.4.algorithm=$w1=-1*range(2,5,1); $w2=range(2,5,1); $d1=range(2,8,1); $d2=range(2,8,1); condition:ne($d1,$d2); $lcd=($d1*$d2)/gcd($d1,$d2); $n1=range(1,$d1-1,1); $n2=range(1,$d2-1,1); condition:ne($n1,$n2); condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); $num1=($w1*$d1-$n1)*$lcd/$d1; $num2=($w2*$d2+$n2)*$lcd/$d2; $num=$num1-$num2; condition:ne($num,0); $cf=$gcd(abs($num),$lcd); $d=$lcd/$cf; $pna=abs($num)/$cf; $wt=int($pna/$d); $n=$pna-$wt*$d; condition:ne($n,0); $w=if(lt($num,0),-1*$wt,$wt); condition:ne($w,0);@ qu.5.4.question= Evaluate :
$w1
$n1
$d1
− $w2
$n2
$d2
= <1>
<2>
<3>

Write your answer as a mixed fraction filling in the boxes.

@ qu.5.4.blank.1=%24w@ qu.5.4.blank.2=%24n@ qu.5.4.blank.3=%24d@ qu.5.4.extra=@ qu.5.4.format.input=text@ qu.6.topic=5_3 Multiply Fractions@ qu.6.1.mode=Blanks@ qu.6.1.name=+ +@ qu.6.1.comment=

Evaluate:
$n1
$d1
•
$n2
$d2
=

Multiply the numerators and denominators.

$num
$den

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}

${$num/$cf}
${$den/$cf}

The answer as an improper fraction is:
$n
$d
@ qu.6.1.editing=useHTML@ qu.6.1.algorithm=$n1=range(2,12,1); $n2=range(2,12,1); $d1=range(2,12,1); $d2=range(2,12,1); condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); $num=$n1*$n2; $den=$d1*$d2; $cf=gcd($num,$den); $n=$num/$cf; $d=$den/$cf; condition:ne(int(abs($n)/$d),abs($n)/$d);@ qu.6.1.question=

Evaluate:
$n1
$d1
•
$n2
$d2
=
<1>
<2>

Write the answer as an improper fraction in reduced form. @ qu.6.1.blank.1=%24n@ qu.6.1.blank.2=%24d@ qu.6.1.extra=@ qu.6.1.format.input=text@ qu.6.2.mode=Blanks@ qu.6.2.name=- +@ qu.6.2.comment=

Evaluate:
$n1
$d1
•
$n2
$d2
=

Multiply the numerators and denominators.

$num
$den

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}

${$num/$cf}
${$den/$cf}

The answer as an improper fraction is:
$n
$d
@ qu.6.2.editing=useHTML@ qu.6.2.algorithm=$n1=-1*range(2,12,1); $n2=range(2,12,1); $d1=range(2,12,1); $d2=range(2,12,1); condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); $num=$n1*$n2; $den=$d1*$d2; $cf=gcd($num,$den); $n=$num/$cf; $d=$den/$cf; condition:ne(int(abs($n)/$d),abs($n)/$d);@ qu.6.2.question=

Evaluate:
$n1
$d1
•
$n2
$d2
=
<1>
<2>

Write the answer as an improper fraction in reduced form. @ qu.6.2.blank.1=%24n@ qu.6.2.blank.2=%24d@ qu.6.2.extra=@ qu.6.2.format.input=text@ qu.6.3.mode=Blanks@ qu.6.3.name=- -@ qu.6.3.comment=

Evaluate:
$n1
$d1
•
$n2
$d2
=

Multiply the numerators and denominators.

$num
$den

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}

${$num/$cf}
${$den/$cf}

The answer as an improper fraction is:
$n
$d
@ qu.6.3.editing=useHTML@ qu.6.3.algorithm=$n1=-1*range(2,12,1); $n2=-1*range(2,12,1); $d1=range(2,12,1); $d2=range(2,12,1); condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); $num=$n1*$n2; $den=$d1*$d2; $cf=gcd($num,$den); $n=$num/$cf; $d=$den/$cf; condition:ne(int(abs($n)/$d),abs($n)/$d);@ qu.6.3.question=

Evaluate:
$n1
$d1
•
$n2
$d2
=
<1>
<2>

Write the answer as an improper fraction in reduced form. @ qu.6.3.blank.1=%24n@ qu.6.3.blank.2=%24d@ qu.6.3.extra=@ qu.6.3.format.input=text@ qu.6.4.mode=Blanks@ qu.6.4.name=+ -@ qu.6.4.comment=

Evaluate:
$n1
$d1
•
$n2
$d2
=

Multiply the numerators and denominators.

$num
$den

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}

${$num/$cf}
${$den/$cf}

The answer as an improper fraction is:
$n
$d
@ qu.6.4.editing=useHTML@ qu.6.4.algorithm=$n1=range(2,12,1); $n2=-1*range(2,12,1); $d1=range(2,12,1); $d2=range(2,12,1); condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); $num=$n1*$n2; $den=$d1*$d2; $cf=gcd($num,$den); $n=$num/$cf; $d=$den/$cf; condition:ne(int(abs($n)/$d),abs($n)/$d);@ qu.6.4.question=

Evaluate:
$n1
$d1
•
$n2
$d2
=
<1>
<2>

Write the answer as an improper fraction in reduced form. @ qu.6.4.blank.1=%24n@ qu.6.4.blank.2=%24d@ qu.6.4.extra=@ qu.6.4.format.input=text@ qu.7.topic=5_3 Multiply Mixed Fractions@ qu.7.1.mode=Blanks@ qu.7.1.name=+ +@ qu.7.1.comment=

Evaluate:

$w1
$nw1
$d1
• $w2
$nw2
$d2
=
Convert mixed fractions to improper fractions.
$n1
$d1
•
$n2
$d2
=

Multiply the numerators and denominators.

$num
$den

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}

${$num/$cf}
${$den/$cf}
Write as a mixed fraction.
$w
$n
$d
@ qu.7.1.editing=useHTML@ qu.7.1.algorithm=$w1=range(2,5,1); $w2=range(2,5,1); $d1=range(2,8,1); $d2=range(2,8,1); $nw1=range(1,$d1-1,1); $nw2=range(1,$d2-1,1); $n1=$w1*$d1+$nw1; $n2=$w2*$d2+$nw2; condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); $num=$n1*$n2; $den=$d1*$d2; $cf=gcd($num,$den); $na=$num/$cf; $d=$den/$cf; condition:ne($num,0); $cf=$gcd(abs($num),$den); $d=$den/$cf; $pna=abs($na); $wt=int($pna/$d); $n=$pna-$wt*$d; condition:ne($n,0); $w=if(lt($num,0),-1*$wt,$wt); condition:ne($w,0); condition:ne($n,0);@ qu.7.1.question=

Evaluate:
$w1
$nw1
$d1
• $w2
$nw2
$d2
= <1>
<2>
<3>

Write the answer as an mixed fraction in reduced form. @ qu.7.1.blank.1=%24w@ qu.7.1.blank.2=%24n@ qu.7.1.blank.3=%24d@ qu.7.1.extra=@ qu.7.1.format.input=text@ qu.7.2.mode=Blanks@ qu.7.2.name=- +@ qu.7.2.comment=

Evaluate:

$w1
$nw1
$d1
• $w2
$nw2
$d2
=
Convert mixed fractions to improper fractions.
$n1
$d1
•
$n2
$d2
=

Multiply the numerators and denominators.

$num
$den

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}

${$num/$cf}
${$den/$cf}
Write as a mixed fraction.
$w
$n
$d
@ qu.7.2.editing=useHTML@ qu.7.2.algorithm=$w1=-1*range(2,5,1); $w2=range(2,5,1); $d1=range(2,8,1); $d2=range(2,8,1); $nw1=range(1,$d1-1,1); $nw2=range(1,$d2-1,1); $n1=$w1*$d1-$nw1; $n2=$w2*$d2+$nw2; condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); $num=$n1*$n2; $den=$d1*$d2; $cf=gcd($num,$den); $na=$num/$cf; $d=$den/$cf; condition:ne($num,0); $cf=$gcd(abs($num),$den); $d=$den/$cf; $pna=abs($na); $wt=int($pna/$d); $n=$pna-$wt*$d; condition:ne($n,0); $w=if(lt($num,0),-1*$wt,$wt); condition:ne($w,0); condition:ne($n,0);@ qu.7.2.question=

Evaluate:
$w1
$nw1
$d1
• $w2
$nw2
$d2
= <1>
<2>
<3>

Write the answer as an mixed fraction in reduced form. @ qu.7.2.blank.1=%24w@ qu.7.2.blank.2=%24n@ qu.7.2.blank.3=%24d@ qu.7.2.extra=@ qu.7.2.format.input=text@ qu.7.3.mode=Blanks@ qu.7.3.name=- -@ qu.7.3.comment=

Evaluate:

$w1
$nw1
$d1
• $w2
$nw2
$d2
=
Convert mixed fractions to improper fractions.
$n1
$d1
•
$n2
$d2
=

Multiply the numerators and denominators.

$num
$den

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}

${$num/$cf}
${$den/$cf}
Write as a mixed fraction.
$w
$n
$d
@ qu.7.3.editing=useHTML@ qu.7.3.algorithm=$w1=-1*range(2,5,1); $w2=-1*range(2,5,1); $d1=range(2,8,1); $d2=range(2,8,1); $nw1=range(1,$d1-1,1); $nw2=range(1,$d2-1,1); $n1=$w1*$d1-$nw1; $n2=$w2*$d2-$nw2; condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); $num=$n1*$n2; $den=$d1*$d2; $cf=gcd($num,$den); $na=$num/$cf; $d=$den/$cf; condition:ne($num,0); $cf=$gcd(abs($num),$den); $d=$den/$cf; $pna=abs($na); $wt=int($pna/$d); $n=$pna-$wt*$d; condition:ne($n,0); $w=if(lt($num,0),-1*$wt,$wt); condition:ne($w,0); condition:ne($n,0);@ qu.7.3.question=

Evaluate:
$w1
$nw1
$d1
• $w2
$nw2
$d2
= <1>
<2>
<3>

Write the answer as an mixed fraction in reduced form. @ qu.7.3.blank.1=%24w@ qu.7.3.blank.2=%24n@ qu.7.3.blank.3=%24d@ qu.7.3.extra=@ qu.7.3.format.input=text@ qu.7.4.mode=Blanks@ qu.7.4.name=+ -@ qu.7.4.comment=

Evaluate:

$w1
$nw1
$d1
• $w2
$nw2
$d2
=
Convert mixed fractions to improper fractions.
$n1
$d1
•
$n2
$d2
=

Multiply the numerators and denominators.

$num
$den

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}

${$num/$cf}
${$den/$cf}
Write as a mixed fraction.
$w
$n
$d
@ qu.7.4.editing=useHTML@ qu.7.4.algorithm=$w1=range(2,5,1); $w2=-1*range(2,5,1); $d1=range(2,8,1); $d2=range(2,8,1); $nw1=range(1,$d1-1,1); $nw2=range(1,$d2-1,1); $n1=$w1*$d1+$nw1; $n2=$w2*$d2-$nw2; condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); $num=$n1*$n2; $den=$d1*$d2; $cf=gcd($num,$den); $na=$num/$cf; $d=$den/$cf; condition:ne($num,0); $cf=$gcd(abs($num),$den); $d=$den/$cf; $pna=abs($na); $wt=int($pna/$d); $n=$pna-$wt*$d; condition:ne($n,0); $w=if(lt($num,0),-1*$wt,$wt); condition:ne($w,0); condition:ne($n,0);@ qu.7.4.question=

Evaluate:
$w1
$nw1
$d1
• $w2
$nw2
$d2
= <1>
<2>
<3>

Write the answer as an mixed fraction in reduced form. @ qu.7.4.blank.1=%24w@ qu.7.4.blank.2=%24n@ qu.7.4.blank.3=%24d@ qu.7.4.extra=@ qu.7.4.format.input=text@ qu.8.topic=5_4 Divide Fractions@ qu.8.1.mode=Blanks@ qu.8.1.name=+ +@ qu.8.1.comment=

Evaluate:

$n1
$d1
 ÷ 
$d2
$n2
=

When dividing, multiply by the reciprocal.
$n1
$d1
 •
$n2
$d2
=

Multiply the numerators and denominators.

$num
$den

Reduce the fraction if possible. ${if(ne($cf,1),"The greatest common factor is $cf.","")}

${$num/$cf}
${$den/$cf}

The answer as an improper fraction is:
$n
$d
@ qu.8.1.editing=useHTML@ qu.8.1.algorithm=$n1=range(2,12,1); $n2=range(2,12,1); $d1=range(2,12,1); $d2=range(2,12,1); condition:eq(gcd($n1,$d1),1); condition:eq(gcd($n2,$d2),1); $num=$n1*$n2; $den=$d1*$d2; $cf=gcd($num,$den); $n=$num/$cf; $d=$den/$cf; condition:ne(int(abs($n)/$d),abs($n)/$d);@ qu.8.1.question=

Evaluate:
$n1
$d1
 ÷ 
$d2
$n2
=
<1>
<2>

Write the answer as an improper fraction in reduced form. @ qu.8.1.blank.1=%24n@ qu.8.1.blank.2=%24d@ qu.8.1.extra=@ qu.8.1.format.input=text@ qu.8.2.mode=Blanks@ qu.8.2.name=+ -@ qu.8.2.comment=

Evaluate:

$n1
$d1
 ÷ 
${-1*$d2}
${-1*$n2}
=

When dividing, multiply by the reciprocal.
$n1
$d1
 •
$n2
$d2
=